基于大地经纬度的二维TDOA无源定位

doi:10.11959/j.issn.1000-436x.2019118

通信学报 ›› 2019, Vol. 40 ›› Issue (5): 136-143.doi: 10.11959/j.issn.1000-436x.2019118

基于大地经纬度的二维TDOA无源定位

马方立^1,^2,³,徐扬^3,⁴,徐鹏^3,⁴

¹ 西南交通大学信息科学与技术学院，四川成都 611756
² 四川省无线电监测站，四川成都 610052
³ 系统可信性自动验证国家地方联合工程实验室，四川成都 610031
⁴ 西南交通大学数学学院，四川成都 611756

修回日期:2019-04-21 出版日期:2019-05-25 发布日期:2019-05-30
作者简介:马方立（1966- ），男，四川成都人，西南交通大学博士生，主要研究方向为无线电监测、信号处理、智能信息处理。|徐扬（1956- ），男，河南新乡人，博士，西南交通大学教授、博士生导师，主要研究方向为逻辑代数、数理逻辑、不确定性推理、自动推理。|徐鹏（1981- ），男，河南新乡人，博士，西南交通大学讲师，主要研究方向为无线网络资源管理、智能信息处理、无线电管理与监测、信息安全。
基金资助:
国家自然科学基金资助项目(61673320);中央高校基本科研业务费专项资金资助项目(2682018ZT10);中央高校基本科研业务费专项资金资助项目(2682018CX59);四川省教育厅科研基金资助项目(18ZB0589)

2D-TDOA passive location based on geodetic longitude and latitude

Fangli MA^1,^2,³,Yang XU^3,⁴,Peng XU^3,⁴

¹ School of Information Science and Technology,Southwest Jiaotong University,Chengdu 611756,China
² Sichuan Provincial Radio Monitoring Station,Chengdu 610052,China
³ National-Local Joint Engineering Laboratory of System Credibility Automatic Verification,Chengdu 610031,China
⁴ School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China

Revised:2019-04-21 Online:2019-05-25 Published:2019-05-30
Supported by:
The National Natural Science Foundation of China(61673320);Scientific Research Foundation of the Education Department of Sichuan Province(18ZB0589)

摘要/Abstract

摘要：

因地球表面并非平面，采用平面坐标的传统TDOA无源定位模型可能存在一定的误差。为了直接利用大地经纬度坐标进行TDOA定位，提出了基于球面两点间距离计算的一系列球面距离计算TDOA定位模型。通过最优化建模，以网格逐点搜索求解法进行模型验证。数值分析结果表明，球面精确计算模型定位误差最小，与纬度无关；球面近似计算模型的定位误差次之，随纬度升高而增加；等距离正圆柱投影模型在低纬度地区定位误差较小，但在中、高纬度地区定位误差大；等角度正圆柱投影模型和等面积正圆柱投影模型的定位误差比较大，在任何纬度时均在26%左右，不可用。

关键词: 无源定位, 到达时间差, 经纬度, 球面精确计算, 球面近似计算

Abstract:

Because of the surface of the earth is not a plane,there may be some errors in the conventional ultra-short wave passive TDOA location method using plane coordinates.In order to use the geodetic longitude and latitude coordinates directly for TDOA location,a series of spherical distance TDOA location models based on spherical two-point distance calculation were proposed.The optimal location models were adopted,and a grid point search method was applied with model validation.The numerical results show that the spherical precise calculation model has the smallest positioning error,which is independent of latitude.Positioning error of the spherical approximation calculation model is worse than the first model,and increases with the increase of latitude.The equidistant orthographic cylindrical projection model has a small positioning error in the low latitudes.However,it has a large positioning error in the middle and high latitudes.The equiangular orthographic cylindrical projection model and the equiareal orthographic cylindrical projection model have a relatively large positioning error,which is around 26% at any latitude and is not applicable.

Key words: passive location, TDOA, longitude and latitude, spherical precise calculation, spherical approximate calculation

中图分类号:

TN802

马方立,徐扬,徐鹏. 基于大地经纬度的二维TDOA无源定位[J]. 通信学报, 2019, 40(5): 136-143.

Fangli MA,Yang XU,Peng XU. 2D-TDOA passive location based on geodetic longitude and latitude[J]. Journal on Communications, 2019, 40(5): 136-143.

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参考文献 17

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φ₀	Δd/km	r
0°	111.2	1.000 0
5°	110.8	0.996 2
10°	109.5	0.984 7
15°	107.4	0.965 9
20°	104.5	0.934 7
25°	100.8	0.906 3
30°	96.3	0.866 0
35°	91.1	0.819 2
40°	85.2	0.766 2
45°	78.6	0.707 1
50°	71.5	0.643 0
55°	63.8	0.573 6
60°	55.6	0.500 0
65°	47.0	0.422 6
70°	38.0	0.341 7
75°	28.8	0.258 8
80°	19.3	0.173 6
85°	9.7	0.087 1

参数	取值
定位网络构成	距离相等的3个监测站点
定位网络中心所处纬度	0o～85o，步长为5o
信号源的位置	在定位网络之内，在经线上等间隔取24个点，在纬线上等间隔取13个点，由于定位网络呈三角形，故共取156个不同的点
考虑时间差测量误差	为-50～50 ns之间的等概率分布，对应距离误差±15 m
搜索网格数量/个	200×200
定位计算结果与信号源实际位置误差的表示方式	求156个定位误差的均方根，并除以基线长度，得到定位误差相对于基线的百分比

基于大地经纬度的二维TDOA无源定位

2D-TDOA passive location based on geodetic longitude and latitude

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